Comments (2)
brendanzab
commented on June 28, 2024
I've been wishing for this too - eg. for having a default typing context for my language. This is a bit related to #100 I think?
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astampoulis
commented on June 28, 2024
Hi @d4hines and @brendanzab !
There isn't a built-in way to define constants right now unfortunately. The situation is a little easier to work-around though compared to type-level constants: you could define a predicate to expand definitions in a term, before doing any other kind of computation (e.g. type-checking, evaluation, etc.).
Here's some code that you could use for now, but I'll see if I can add something like this to the standard library, or to the core eventually.
define : [A] A -> A -> prop.
expand_definitions, expand_definitions_aux : [A] A -> A -> prop.
expand_definitions X Y :-
demand.case_otherwise
(expand_definitions_aux X Y)
(structural @expand_definitions X Y).
expand_definitions_aux D E when (define D E).
(* STLC *)
term : type.
lam : (term -> term) -> term.
app : term -> term -> term.
typ : type.
arrow : typ -> typ -> typ.
typecheck : term -> typ -> prop.
typecheck (lam E) (arrow T T') :-
(x:term -> typecheck x T -> typecheck (E x) T').
typecheck (app E1 E2) T' :-
typecheck E1 (arrow T T'), typecheck E2 T.
(* church numerals as example of definitions *)
intconst : int -> term.
define (intconst 0) (lam (fun z => lam (fun s => z))).
define (intconst N) (lam (fun z => lam (fun s => app s (Pred z s))))
when lessthan 0 N true :-
minus N 1 N',
define (intconst N') (lam (fun z => lam (fun s => Pred z s))).
(expand_definitions (intconst 2) X, typecheck X Y) ?
There is an alternative approach, which is not common in textbooks: you could extend the base language with a constructor for using a definition, and then add a typing rule for those, that "looks up" the definition itself. Here's one way to do that:
(* STLC *)
term : type.
lam : (term -> term) -> term.
app : term -> term -> term.
typ : type.
arrow : typ -> typ -> typ.
typecheck : term -> typ -> prop.
typecheck (lam E) (arrow T T') :-
(x:term -> typecheck x T -> typecheck (E x) T').
typecheck (app E1 E2) T' :-
typecheck E1 (arrow T T'), typecheck E2 T.
(* add definitions *)
def : term -> term.
define : term -> term -> prop.
typecheck (def X) T :-
define X Y, typecheck Y T.
intconst : int -> term.
define (intconst 0) (lam (fun z => lam (fun s => z))).
define (intconst N) (lam (fun z => lam (fun s => app s (Pred z s))))
when lessthan 0 N true :-
minus N 1 N',
define (intconst N') (lam (fun z => lam (fun s => Pred z s))).
(typecheck (def (intconst 0)) Y) ?
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Related Issues (20)
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